Pertanyaan

y → 2 lim ( y + 4 4 y 3 + 8 y ) 3 1 = ...

$y \to 2 lim (\frac{4 y ^{3} + 8 y}{y + 4})^{\frac{1}{3}} = ...$

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan perhitungan berikut. Ingat: Maka: Jadi, nilai limit tersebut adalah mendekati 2. Dengan demikian, jawaban yang tepat adalah D.

Perhatikan perhitungan berikut.

Ingat:

$begin mathsize 14px style limit as x rightwards arrow c of fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction equals fraction numerator limit as x rightwards arrow c of f open parentheses x close parentheses over denominator limit as x rightwards arrow c of g open parentheses x close parentheses end fraction end style$

Maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as y rightwards arrow 2 of open parentheses fraction numerator 4 y cubed plus 8 y over denominator y plus 4 end fraction close parentheses to the power of 1 third end exponent end cell equals cell open parentheses fraction numerator 4 open parentheses 2 close parentheses cubed plus 8 open parentheses 2 close parentheses over denominator 2 plus 4 end fraction close parentheses to the power of 1 third end exponent end cell row blank equals cell open parentheses fraction numerator 4 times 8 plus 16 over denominator 6 end fraction close parentheses to the power of 1 third end exponent end cell row blank equals cell open parentheses fraction numerator 32 plus 16 over denominator 6 end fraction close parentheses to the power of 1 third end exponent end cell row blank equals cell open parentheses 48 over 6 close parentheses to the power of 1 third end exponent end cell row blank equals cell open parentheses 8 close parentheses to the power of 1 third end exponent end cell row blank equals cell open parentheses 2 cubed close parentheses to the power of 1 third end exponent end cell row blank equals cell 2 to the power of 3 times 1 third end exponent end cell row blank equals 2 end table end style$

Jadi, nilai limit tersebut adalah mendekati 2.

Dengan demikian, jawaban yang tepat adalah D.